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lfunc_lfunctions • Show schema
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{'Lhash': '1256956355364689481153801494948', 'a10': [0.401695234366993, 1.7599418140662888], 'a2': [1.1255250354658461, -1.4113637535205792], 'a3': [-0.2225209339563144, 0.9749279121818236], 'a4': [-0.2800991713786752, -1.2271946531092726], 'a5': [-0.6234898018587335, 0.7818314824680298], 'a6': [1.1255250354658461, 1.4113637535205792], 'a7': [-0.8635625828834036, 3.7835148855439584], 'a8': [1.2055849175513629, 0.5805790971099034], 'a9': [-0.9009688679024191, -0.4338837391175581], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.4734924879256983, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.2225209339563144, -0.9749279121818236]]], [5, [[1.0, 0], [0.6234898018587335, -0.7818314824680298]]], [29, [[1.0, 0], [3.017172688465918, 4.460568233754008]]]], 'bad_primes': [3, 5, 29], 'central_character': '435.226', 'coefficient_field': 'CDF', 'conductor': 435, 'conductor_radical': 435, 'conjugate': 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- 0.4858753751019871*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0807495570368', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.991563728316292742569864583807', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '3.32131981478803806694359449494', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.49724621762130877625333249533', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.4734924879256983, 'bad_primes': [3, 5, 29], 'central_character': '29.23', 'conductor': 435, 'conductor_radical': 435, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/435/2/u/a/226/4'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-435-29.23-c1-0-7', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-435-29.23-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8637307981373539, 'root_angle': -0.08074955703680362, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.991563728316292742569864583807', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1256956355364689481153801494948', 'Lhash_array': ['1256956355364689481153801494948'], 'factors': ['2-435-29.23-c1-0-7'], 'label': '2-435-29.23-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/435/2/u/a/226/4'}